An indicator preselection based evolutionary algorithm with auxiliary angle selection for many-objective optimization

Many-objective evolutionary algorithms (MaOEAs) have received significant achievements in recent years. Maintaining a balance between convergence and diversity becomes a key challenge for many-objective evolutionary algorithms when the number of optimization objectives increases. To address this issue, we propose a many-objective evolutionary algorithm using the indicator preselection and auxiliary angle selection (PSEA). In PSEA, a unit vector-based indicator is proposed to pre-select the population region for increasing selection pressure and maintaining diversity simultaneously, which is utilized to identify a promising region in the objective space. Due to the poor quality of individuals outside the promising region, these individuals in the current population can be temporarily discarded. Then, to ensure the diversity of the population, a new strategy based on the second auxiliary angle strategy is designed to calculate the neighborhood density. Finally, in the environmental selection, these strategies are employed for selecting individuals with good convergence and diversity from the candidate set one by one to enter the next generation. The experimental results on commonly used benchmark test problems and many-objective traveling salesman problems with objectives varying from 5 to 20 have demonstrated that PSEA outperforms some state-of-the-art approaches.